Oscillatory criteria of general nonlinear hyperbolic equations with continuous deviating arguments (Q1406095)

The authors use averaging technique to study oscillatory properties of the following nonlinear hyperbolic equation \[ \frac{\partial^2}{\partial t^2}[u + \lambda(t)u(x,t-\tau)] = a(t)\Delta u - c(x,t,u) - \int_a^b q(x,t,\xi)f(t,u(x,g(t,\xi))) d \sigma (\xi), \] together with boundary conditions of Dirichlet or mixed type. Sufficient conditions for the oscillation of the solutions are obtained.